Transport equations for waves in a half Space

We derive boundary conditions for the phase space energy density of acoustic waves in a half space, in the high frequency limit. These boundary conditions generalize the usual reflection—transmission relations for plane waves and are well suited for the study of wave propagation in bounded randed random media in the radiative transport approximation[15]. The high frequency analysis is based on direct calculations with Fourier integrals in the case of constant coefficients and Wigner measures in general, and it is presented in detail

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